The entanglement of purification (EoP) is another quantity which measures the total correlation between two disjoint subsystems \(A\)  and \(B\)  for mixed state \(\rho _{AB}\)  [1]}, [2]}. In general, by enlarging the Hilbert space we can purify a mixed state. In fact, purification refers to the fact that every mixed state acting on the Hilbert spaces can be viewed as the reduced state of some pure states. The EoP is defined by the minimum of the EE between subsystems \(AA^{\prime }\)  and \(BB^{\prime }\)  against all possible purifications where \(A^{\prime }\)  and \(B^{\prime }\)  are arbitrary. Obviously, when two subsystems \(A\)  and \(B\)  are complementary to each other, the EoP between two subsystems reduces to the EE of subsystem \(A\) . It is very difficult to compute the EoP in QFT, however it has been computed by numerical lattice calculation in QFT [3]}, [4]}, [5]}. It has been conjectured that the EoP is holographically dual to the minimal cross-section of entanglement wedge \(E_w\)  of \(\rho _{AB}\) , which satisfies the basic properties of the EoP [6]}, [7]}. \(E_w\)  of \(\rho _{AB}\)  is reduced to the holographic entanglement entropy (HEE), when the total system \(A\cup B\)  is pure. In the literature, other correlation measures such as reflected entropy, odd entropy and logarithmic negativity are discussed and all of them are connected with the entanglement wedge cross-section [8]}, [9]}, [10]}. Various aspects of the EoP are discussed in the literature, for example, see [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}, [24]}, [25]}, [26]}, [27]}, [28]}, [29]}, [30]}, [31]}, [32]}, [33]}, [34]}, [35]}, [36]}, [37]}, [38]}
